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7 - Advanced Field Theory Topics

from Part II - Infrared Behavior, 2PI, I/N, Backreaction and Semiclassical Gravity

Published online by Cambridge University Press:  20 January 2020

Bei-Lok B. Hu
Affiliation:
University of Maryland, College Park
Enric Verdaguer
Affiliation:
Universitat de Barcelona
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Summary

In this chapter we construct the closed-time-path (CTP) two-particle-irreducible (2PI) effective action to two-loop order. The CTP formalism introduced in Chapter 3 is needed to track the dynamics of expectation values and to produce real and causal equations of motion. The composite particle or 2PI formalism introduced in Chapter 6 is needed to treat critical phenomena, because the correlation function and the mean field act as independent variables, instead of the former being a derivative of the latter, as in the 1PI formulation. The large N expansion has the advantage of yielding nonperturbative evolution equations in the regime of strong mean field and a covariantly conserved stress-energy tensor. To leading order in large N, the quantum effective action for the matter fields can be interpreted as a leading-order term in the expansion of the full matter plus gravity quantum effective action, which produces equations of motion for semiclassical gravity and, at the next-to-leading order in large N, stochastic gravity. Two types of quantum fields are treated: (a) O(N) self-interacting Phi-4 fields, and (b) Yukawa coupling between scalar and spinor fields, as an example of dealing with fermions in curved spacetime.

Type
Chapter
Information
Semiclassical and Stochastic Gravity
Quantum Field Effects on Curved Spacetime
, pp. 228 - 264
Publisher: Cambridge University Press
Print publication year: 2020

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